This article reviews the Bayesian inference with the Monte Carlo Markov Chain (MCMC) and the Hamiltonian Monte Carlo (HMC) samplers as a competitor of the classical likelihood statistical inference for pharmacometricians. The MCMC and the HMC samplers have greatly contributed to realization of the Bayesian methods with minimal requirement of mathematical theory. They do not require any closed form of the posterior density nor linear approximation of complex nonlinear models in high dimension even with non-conjugate priors. The HMC even weakens the dependency of the chain and improves computational efficiency. Pharmacometrics is one of great beneficiaries since they use complex multivariate multilevel nonlinear mixed effects models based on the restricted maximum likelihood estimation. Comprehension of the Bayesian approach will help pharmacometricians to access the data analysis more conveniently.

For pharmacometricians, probability theory is the very first obstacle towards the statistics since it is solely founded on mathematics. The purpose of this tutorial is to provide a simple version of introduction to a univariate random variable, its mean, variance, and the correlation coefficient of two random variables using as simple mathematics as possible. The definitions and theorems in this tutorial appear in most of the statistics books in common. Most examples are small and free of subjects like coins, dice, and binary signals so that the readers can intuitively understand them.
Mathematics ; Numismatics ; Probability Theory

The maximum likelihood estimator is the point estimator of the top priority in statistical data analysis because of its optimum properties for large sample size. While the maximum likelihood estimator is widely used, it has been an abstruse subject for pharmacometricians without statitics bagkround because of high dimensional calculus and asymptotic theories. This tutorial provides a general and brief introduction to the maximum likelihood estimator and its related caluculus for non-statisticians.
Calculi ; Data Interpretation, Statistical ; Sample Size

The structural complexity of crossover studies for bioequivalence test confuses analysts and leaves them a hard choice among various programs. Our study reviews PROC GLM and PROC MIXED in SAS and compares widely used SAS codes for crossover studies. PROC MIXED based on REML is more recommended since it provides best linear unbiased estimator of the random between-subject effects and its variance. Our study also considers the covariance structure within subject over period which most PK/PD studies and crossover studies ignore. The QT interval data after the administration of moxifloxacin for a fixed time point are analyzed for the comparison of representative SAS codes for crossover studies.
Cross-Over Studies* ; Therapeutic Equivalency

Statistical analysts engaged in typical clinical trials often have to confront a tight schedule to finish massive statistical analyses specified in a Standard Operation Procedure (SOP). Thus, statisticians or not, most analysts would want to reuse or slightly modify existing programs. Since even a slight misapplication of statistical methods or techniques can easily drive a whole conclusion to a wrong direction, analysts should arm themselves with well organized statistical concepts in advance. This paper will review basic statistical concepts related to typical clinical trials. The number of variables and their measurement scales determine an appropriate method. Since most of the explanatory variables in clinical trials are designed beforehand, the main statistics we review for clinical trials include univariate data analysis, design of experiments, and categorical data analysis. Especially, if the response variable is binary or observations collected from a subject are correlated, the analysts should pay special attention to selecting an appropriate method. McNemar's test and multiple McNemar's test are respectively recommended for comparisons of proportions between correlated two samples or proportions among correlated multi-samples.
Appointments and Schedules ; Arm ; Chi-Square Distribution ; Cross-Over Studies ; Statistics as Topic ; Weights and Measures